TITLE: "What if" math joke: the derivative of $\ln(x)^e$
QUESTION [26 upvotes]: Randall Munroe, the creator of xkcd in his latest book What if writes (p. 175) that the mathematical analog of the phrase "knock me over with a feather" is seeing the expression $ \ln( x )^{e}$. And he writes regarding this expression: "it's not that, taken literally, it doesn't make sense - it's that you can't imagine a situation where this would apply."
In the footer (same page) he also states that "if you want to be mean to first year calculus students, you can ask them to take the derivative of $ \ln( x )^{e}$. It looks like it should be "$1$" or something but it's not."
I don't get the joke. I think I am not understanding something correctly and I'm not appreciating the irony. Any help?

REPLY [2 votes]: In former times we wrote $\sin x$, $\sin^2 x$, $\sin(2x)$. Then came Mathematica requiring us to write ${\tt Sin[x]}$, which is fine; but at the same time we are allowed to interpret ${\tt Sin[x]^2}$ as ${\tt (Sin[x])^2}$, which is not so obvious.
Therefore it is not at all clear what is meant by $\ln (x)^e$ outside of Mathematica. Is it $\log x^e$, $\bigl(\log x\bigr)^e$, or even something else? In any case: $\ \ln (x)^e$ is bad typography.